|Preprint-No.:||< 363 >||Published in:||April 2013||PDF-File:||IGPM363_k.pdf|
|Title:||Adaptive Near-Optimal Rank Tensor Approximation for High-Dimensional Operator Equations|
|Authors:||Markus Bachmayr, Wolfgang Dahmen|
We consider a framework for the construction of iterative schemes for operator equations that combine low-rank approximation in tensor formats and adaptive ap- proximation in a basis. Under fairly general assumptions, we obtain a rigorous con- vergence analysis, where all parameters required for the execution of the methods depend only on the underlying infinite-dimensional problem, but not on a concrete discretization. Under certain assumptions on the rates for the involved low-rank ap- proximations and basis expansions, we can also give bounds on the computational complexity of the iteration as a function of the prescribed target error. Our theo- retical findings are illustrated and supported by computational experiments. These demonstrate that problems in very high dimensions can be treated with controlled solution accuracy.
|Keywords:||Low–rank tensor approximation, adaptive methods, high–dimensional operator equations, computational complexity|
|Publication:||Foundations of Computational Mathematics |
Oberwolfach reports : OWR 10(3), 2179-2257 (2013)